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For question in Proof Theory, where "proofs" themselves are the object of mathematical investigation. It is not to be used to request a proof of some result.

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Is the union of two conservative extensions of a theory conservative?

As Emil pointed out, assuming $\Sigma=\Sigma_1\cap\Sigma_2$, the union of 2 such theories is always conservative extension, Emil had proven it using the standard formulation Robinson’s joint consisten …
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